A nomogram is a graphic computing device defined as three numeric axes dimensioned and arranged in such a way that an arbitrary straight line will intersect the axes at values that are correlated by some specific mathematical function. In other words, the three axes are the loci of three variables that are correlated by some specific mathematical function so that three points on the lines which simultaneously satisfy the function form a straight line when connected.
Nomograms are capable of reducing the dimensionality of a solution space. Given, for example, two axes representing, respectively, numerators (n) and denominators (d) of a division (n/d), the solution space of the division can be said to be two-dimensional, since each value on each axis combines with each value on the other axis. If the axes are arranged as Cartesian coordinates, the locus of all solutions is the entire area of the coordinate system. The locus of equivalent solutions is a straight line starting at the origin. If the two axes are arranged nomographically, however, the locus of equivalent solutions collapses from a straight line to a point and the locus of all solutions collapses from an area to a line. This line is the third axis of the nomogram.
Solving two determined values for a third dependent value by means of a nomogram consists in drawing a straight line through the two determined values, each on its own axis, and reading the dependent value off the third axis where the straight line intersects. This property has two practical advantages. The first one is that a nomographic solution presents a picture whose interpretation requires far less abstract intelligence than the interpretation of an arithmetic or tabular solution: the numbers and their interdependence are intuitively comprehensible from the picture. The second advantage is that the function solves in all directions with equal ease, no matter which of the three variables is the unknown that depends on the other two.
The two advantages combine to render nomograms particularly useful for finding solutions, not so much for two predetermined values as for functional sets of undetermined values that should conform to certain incidental requirements. Mathematically intractable dependencies of this kind occur often in practical engineering. They must be solved by iterative experimentation. Iterative experimentation by means of a nomogram amounts to shifting a ruler around and assessing the quality of the values at three intersections in terms of the design objective, a fairly straightforward approach that is also expedient on account of the fact that the scales suggest which way the ruler should be moved to improve an unsatisfactory position.